Given time series data \(X_1, \ldots , X_N\) , we can compute an empirical version \(\hat{\gamma }(k)\)  of the ACF: empirical correlation between \(X_1, \ldots , X_{N-k}\)  and \(X_{k+1}, \ldots , X_N\) . Under broad conditions, this is a consistent and asymptotically normal estimate for the true ACF, [1]}.
